To review the role of Monte Carlo simulation in PK/PD target attainment in establishing a dosage regimen

(susceptibility breakpoints)

What is the origin of the word Monte Carlo?ToulouseMonte-Carlo(Monaco)Monte Carlo simulation

The term Monte Carlo was coined by Ulman & van Neumann during their work on development of the atomic bomb after city Monte Carlo (Monaco) on the French Riviera where the primary attraction are casinos containing games of chance

Roulette wheels, dice.. exhibit random behavior and may be viewed as a simple random number generator

What is Monte Carlo simulationsMCs is the term applied to stochastic simulations that incorporate random variability into a model

MCs repeatedly simulatethe model each time drawing a different set of values (inputs) from the sampling distribution of the model parameters, the result of which is a set of possible outcomes (outputs)

Monte Carlo simulation: applied to PK/PD modelsModel: AUC/MICPDF of AUCGenerate random AUC and MIC values across the AUC & MIC distributions that conforms to their probabilitiesPDF of MICCalculate a large number of AUC/MIC ratiosPDF of AUC/MICPlot results in a probability chart% target attainment(AUC:MIC, T>MIC)Adapted from Dudley, Ambrose. Curr Opin Microbiol2000;3:515−521 Monte Carlo simulation for antibiotics

Introduced to anti-infective drug development by Drusano (1998)

to explore the consequences of PK and PD variabilities on the probability of achievement of a given therapeutic target

Time out of the MSW should be higher than 12h (50% of the dosing interval) in 90% of pigs

Step 2: Determination of the AUC/MIC clinical breakpoint value for the new quinolone in pigs The PK/PD index is known (AUC/MIC) for quinolones but its breakpoint values for metaphylaxis (control) or curative treatments have to be either determined experimentally or assumedDetermination of the PK/PD clinical breakpoint value

Dose titration in field trials :

4 groups of 10 animals

Blood samples were obtained

MIC of the pathogen is known

Possible to establish the relationship between AUC/MIC and the clinical success

Dose to selectedDetermination of the PK/PD clinical breakpoint value from the dose titration trialResponseNS*

Blood samples were obtained

MIC of the pathogen is known

Possible to establish the relationship between AUC/MIC and the clinical success

Search optimal solution (e.g. dose) by finding the best combination of decision variables for the best possible results

Metaphylaxis: dose to achieve a POC of 90% i.e. an AUC/MIC of 80(empirical antibiotherapy)Dose distributionComputation of the dose: metaphylaxis(dose=2mg/kg from the dose titration)Sensitivity analysis

Analyze the contribution of the different variables to the final result (predicted dose)

Allow to detect the most important drivers of the model

Sensitivity analysisMetaphylaxis, empirical antibiotherapyContribution of the MIC distributionComputation of the dose using Monte Carlo simulationMetaphylaxis,Targeted antibiotherapyMIC=1µg/mLLog normal distribution: 9±2.07 mL/Kg/hBPmetaphylaxisDose to POC=0.9Uniform distribution: 0.3-0.70Computation of the dose using Monte Carlo simulationTargeted antibiotherapyComputation of the dose: metaphylaxis(dose=2mg/kg from the dose titration)Sensitivity analysis(metaphylaxis, targeted antibiotherapy)F%Computation of the dose (mg/kg):metaphylaxis vs. curative & empirical vs. targetedThe variance–covariance matrixThe second criteria to determine the optimal dose: the MSW & MPCKinetic disposition of the new quinolone for the selected metaphylactic dose (3.8 mg/kg)(monocompartmental model, oral route)Log normal distribution: 9±2.07 mL/kg/hF%Uniform distribution: 0.3-0.70Slope=Cl/Vc=0.09 per h (T1/2=7.7h)MPCMICconcentrationsMSWTime>MPC for the POC 90% for metaphylaxis (dose 3.8 mg/kg, empirical antibiotherapy)Time>MPC for the POC 90% for metaphylaxis (dose of 7.1mg/kg, empirical antibiotherapy)Sensitivity analysis (dose of 7.1mg/kg, metaphylaxis, empirical antibiotherapy)Clearance (slope) is the most influential factor of variability for T>MPC ,not bioavailability as for the AUC/MICTime>MPC for the POC 90% for curative treatment(dose of 3.8mg/kg,curative treatmentSensitivity analysis (dose of 3.8mg/kg, curative treatment empirical antibiotherapy)ClearanceClearance (slope) is the only influential factor of variability for T>MPC not bioavailability as for metaphylaxisComputation of the dose (mg/kg):metaphylaxis vs. curative treatmentConclusionconclusions

MCs allow to explore explicitly early in drug development both PK and microbiological (MIC) variabilities to evaluate how often such a target is likely to be achieved after different doses of a drug

The weak link in MCs is Absence of a priori knowledge on PK & PD distribution

Population PK are needed to document influence of different factors on drug exposure

Health vs. disease; age; sex; breed…

PD: MIC distributions

Truly representative of real world (prospective rather than retrospective sampling)

Possibility to use diameters distribution if the calibration curve is properly defined

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